Scaling Laws for the Critical Rupture Thickness of Common Thin Films by

Abstract. Despite decades of experimental and theoretical investigation on thin films, considerable uncertainty exists in the prediction of their critical rupture thickness. According to the spontaneous rupture mechanism, common thin films become unstable when capillary waves at the interfaces begin to grow. In a horizontal film with symmetry at the midplane, unstable waves from adjacent interfaces grow towards the center of the film. As the film drains and becomes thinner, unstable waves osculate and cause the film to rupture. Uncertainty stems from a number of sources including the theories used to predict film drainage and corrugation growth dynamics. In the early studies, the linear stability of small amplitude waves was investigated in the context of the quasi-static approximation in which the dynamics of wave growth and film thinning are separated. The zeroth order wave growth equation of Vrij predicts faster wave growth rates than the first order equation derived by Sharma and Ruckenstein. It has been demonstrated in an accompanying paper that film drainage rates and times measured by numerous investigations are bounded by the predictions of the Reynolds equation and the more recent theory of Manev, Tsekov, and Radoev. Solutions t